At my work we have a SharePoint server. Whenever I would open a document (.docx, .xlsx) it would always open in Read Only mode. I found a fix for this that worked for me (Windows 7 x64 and Office 2007).
First we need to open the registry editor. Go to Start>Run and type in: regedit and click OK. If you are on Windows 7 and do not have a Run box do this:
Start>All Programs>Accessories>right click on Command Prompt and choose 'Run as Administrator'. This will bring up a command prompt window. At the prompt type: regedit and hit the Enter key. This should open the registry editor.
Now expand to the following registry key: HKEY_CURRENT_USER\Software\Microsoft\Office\12.0\Common\Internet
With Internet highlighted right click in the white space of the right side window pane and choose 'New>Dword value'. Name the new value OpenDocumentsReadWriteWhileBrowsing
Now right click on the new name and choose Modify. Put 1 in the Value data box. Click Ok.
You should now have something that looks like this:
Once this setting is complete retry opening a document or spreadsheet from the SharePoint server and see if now it opens in an non-read only mode. This worked for me, I hope it works for you.